Synthesis of Dip-Ramp-Plateau, black holes and a semi-classical analysis

Abstract

We consider a probe scalar field in a black hole geometry with a stretched horizon. This horizon provides a cut-off and allows us to compute the normal modes of the probe scalar field. We will demonstrate how the corresponding scalar spectrum, despite exhibiting no evidence of conventional level-repulsion in the spectrum, shows a clear indication of a robust Dip-Ramp-Plateau structure in the corresponding Spectral Form Factor. This behaviour is expected from a full quantum description of a black hole, which we currently lack. We will further discuss several related intriguing features in this set up and comment on possible future directions.